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Construction and box dimension of the composite fractal interpolation function

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  • Dai, Zhong
  • Liu, Shutang

Abstract

In this paper, we construct the composite fractal interpolation function and prove that the compositeness of two general fractal interpolation functions is still a fractal interpolation function. And its generating iterated function system is obtained from given iterated function systems. Finally, the box dimension of the composite fractal interpolation function is discussed. We give an inequality estimate of the upper and lower box dimensions of the composite fractal interpolation function.

Suggested Citation

  • Dai, Zhong & Liu, Shutang, 2023. "Construction and box dimension of the composite fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s096007792300156x
    DOI: 10.1016/j.chaos.2023.113255
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    References listed on IDEAS

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    1. Luor, Dah-Chin, 2020. "On the distributions of fractal functions that interpolate data points with Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Luor, Dah-Chin, 2018. "Fractal interpolation functions for random data sets," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 256-263.
    3. Ri, Songil, 2019. "New types of fractal interpolation surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 291-297.
    4. Kangle Wang, 2022. "Exact Traveling Wave Solution For The Fractal Riemann Wave Model Arising In Ocean Science," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-8, November.
    5. Kangle Wang, 2022. "Exact Traveling Wave Solutions For The Local Fractional Kadomtsov–Petviashvili–Benjamin–Bona–Mahony Model By Variational Perspective," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-7, September.
    6. Luor, Dah-Chin, 2019. "On some qualitative analysis for a new class of fractal interpolants," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 55-62.
    7. Kangle Wang, 2022. "A Novel Perspective To The Local Fractional Bidirectional Wave Model On Cantor Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-7, September.
    8. Ri, SongIl, 2019. "DUPLICATE: New types of fractal interpolation surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 52-58.
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    Cited by:

    1. Agathiyan, A. & Gowrisankar, A. & Fataf, Nur Aisyah Abdul, 2024. "On the integral transform of fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 209-224.

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